Often people mistakenly claim that "God" was crucified for our sin. Yet, God does not have flesh and blood:

And Jesus answered him, "Blessed are you, Simon Bar-Jonah! For flesh and blood has not revealed this to you, but My Father Who is in heaven." -- Matthew 16:17 (ESV)

and when the Samaritan woman argue with Jesus about which race God is:

Jesus said to her, “Woman, believe me, the hour is coming when neither on this mountain nor in Jerusalem will you worship the Father. You worship what you do not know; we worship what we know, for salvation is from the Jews. But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him.

God is spirit, and those who worship him must worship in spirit and truth.”

The woman said to him, “I know that Messiah is coming (he who is called Christ). When he comes, he will tell us all things.”

Jesus said to her, “I who speak to you am he.” -- John 4:21-26 (ESV)

Jesus tells the woman that "God is spirit" and he is the "Messiah" (Christ). Nobody every said that God is "the Messiah".

Paul wrote:

To the King of the ages, immortal, invisible, the only God, be honor and glory forever and ever. -- 1 Timothy 1:17 (ESV)

This implies that God does not have mortal visible blood.

Moses wrote:

But, He (YHVH) said, “you cannot see my face, for man shall not see me and live.” -- Exodus 33:20 (ESV)

Bad translations

Some critiques would quote:

Be shepherds of the church of God, which he bought with his own blood. -- Acts 20:28 (NIV)

While other translate it as:

to feed the church of the Lord which he purchased with his own blood. -- Acts 20:28 (ASV)

Because of these translation people debate on whether the church should be called "the church of God" or "the church of the Lord Jesus".

However, scholars agree that an important part of this verse is deliberately left out. For example see the footnote in the NIV:

‘the blood of his own one,’ a term of endearment (such as ‘his own dear one’) referring to His own son